Your second sentence, popotla, and the one given as correct answer in your book would sound to me most natural. 1. and 3. I would only say if I wanted to really stress ganz spontan und zu Doris. As for the commas I am with dubitans in that they are superfluous, or simply wrong - if one may say so in our times of fanatical descriptivism ;-)

To me "Wir sind letzen Monat ganz spontan zu Doris geflogen" doesn't sound unbalanced, unnatural, and bookish at all.
All your sentences are correct except for the commas. I'm sure no commas are required in E.g 1 and 2. I'm not quite sure about 3, but I think there isn't a comma required. Maybe another native can comment on the commas.

Now to your question: Many exercises are poorly written and only allow one option, although other options are as correct as the option suggested in the answer key. This might be good for beginners, who are supposed to learn the basic and the most common language structures (word orders in this case). But the better and the more experienced you get in a language, the less you need to stick to the basic structures. < ... >

To me "Wir sind letzen Monat ganz spontan zu Doris geflogen" doesn't sound unbalanced, unnatural, and bookish at all.
All your sentences are correct except for the commas. I'm sure no commas are required in E.g 1 and 2. I'm not quite sure about 3, but I think there isn't a comma required. Maybe another native can comment on the commas [...]

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The comma is not only not required but wrong.
(I tried to find an interpretation where the comma is allowed here but could not.)
I'm sure no comma is valid in 1...3 in standard language. (Of course you have "freedom of poets" to spell as you like).

Two commas are possible in 2 to build a kind of brackets - but at another place.
2.1. Letzten Monat sind wir, ganz spontan, zu Doris geflogen.

Thanks. If that sentence sounds natural, balanced etc. to you, then that's what it is.

German punctuation and English punctuation overlap surprisingly little. It will take me a while yet to get used to the idea that in German, one can string together what are in fact a series of complete sentences just by using commas. Full stops? Nowhere in sight! To do that in English is incorrect. (Yes, I'm being very prescriptive but feel that's justified in this case.)

****What is "the usual" (i.e. unmarked) order for time/manner/place etc. clauses? Is it when, then how, then where?

It may help you to know that in a "neutral" sentence (ie. you're not trying to emphasize any part more than another; just considering the normal frequency), the word order in German is the reverse of English. In German, the order is Time → Manner → Place, whereas in English we structure it Place → Manner → Time.Wir sind letzten Monatganz spontanzu Doris geflogen = We flew to Doris'squite spontaneouslylast month. Of course, for stylistic reasons and questions of emphasis, this word order can vary greatly. In you'd like to learn more about this, I'd suggest Hammer's German Grammar and Usage by Martin Durrell, Chapter 21.6.2., which has an excellent explanation of the extended order of adverbials and examples of the variations.

As for the punctuation, you just have to learn the German rules. It's an integral part of the "grammar" of writing. Our way is not necessary better or worse than theirs. Not using the symbols correctly can lead to many a misunderstanding and is thus indeed wrong by the German prescriptive standard. Abandon your preconceived notions and embrace the language for what it is. You'll have a better time of it in the end.

Yes, the general rule for T-M-P order is useful. I came across another example. The "book answer" is Die Reifen brauchen manchmal Luft; I'd thought that Manchmal brauchen die Reifen Luft sounded OK.

I find that when speaking, it's often easier to put part of the utterance before (what becomes the) reverse-order "verb-subject". The reason this is so is that there's less need to "worry" about the T-M-P order of what still remains to be said. (I hope that's clear.)